What are the faces with dotted patterns on them that seemingly cannot be subdivided
The dots mean the face is Active. See Why does one of the faces show dotted in editmode?

The reason why it apparently can't be subdivided is not due to it's selection state, but rather because it is an n-gon. An n-gon is a faces made up of more than four edges.

Subdividing an n-gon won't create edges running through it, but will still add vertices to it's existing edges:



While in Face Select mode these verts won't be visible. To see them, switch to Vertex Select mode
(&#9096; Ctrl&#8633; Tab).

Depending on what you are doing, n-gons should generally be avoided. See When should N-Gons be used, and when shouldn&#39;t they? for some more info.